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Atomistic simulation of surface functionalization on the interfacial properties ofgraphene-polymer nanocompositesM. C. Wang, Z. B. Lai, D. Galpaya, C. Yan, N. Hu, and L. M. Zhou

Citation: Journal of Applied Physics 115, 123520 (2014); doi: 10.1063/1.4870170 View online: http://dx.doi.org/10.1063/1.4870170 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/115/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Broadband saturable absorption and optical limiting in graphene-polymer composites Appl. Phys. Lett. 102, 191112 (2013); 10.1063/1.4805060 Microwave and mechanical properties of quartz/graphene-based polymer nanocomposites Appl. Phys. Lett. 102, 072903 (2013); 10.1063/1.4793411 Enhanced dielectric properties of BaTiO3/poly(vinylidene fluoride) nanocomposites for energy storageapplications J. Appl. Phys. 113, 034105 (2013); 10.1063/1.4776740 The importance of bendability in the percolation behavior of carbon nanotube and graphene-polymer composites J. Appl. Phys. 112, 066104 (2012); 10.1063/1.4752714 Raman study of interfacial load transfer in graphene nanocomposites Appl. Phys. Lett. 98, 063102 (2011); 10.1063/1.3552685

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Atomistic simulation of surface functionalization on the interfacial propertiesof graphene-polymer nanocomposites

M. C. Wang,1 Z. B. Lai,1 D. Galpaya,1 C. Yan,1,a) N. Hu,2 and L. M. Zhou3

1School of Chemistry, Physics and Mechanical Engineering, Science and Engineering Faculty,Queensland University of Technology, 2 George Street, G.P.O. Box 2434, Brisbane, Australia2Department of Engineering Mechanics, College of Aerospace Engineering, Chongqing University,Chongqing, China3Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China

(Received 12 February 2014; accepted 20 March 2014; published online 28 March 2014)

Graphene has been increasingly used as nano sized fillers to create a broad range of

nanocomposites with exceptional properties. The interfaces between fillers and matrix play a

critical role in dictating the overall performance of a composite. However, the load transfer

mechanism along graphene-polymer interface has not been well understood. In this study, we

conducted molecular dynamics simulations to investigate the influence of surface functionalization

and layer length on the interfacial load transfer in graphene-polymer nanocomposites. The

simulation results show that oxygen-functionalized graphene leads to larger interfacial shear force

than hydrogen-functionalized and pristine ones during pull-out process. The increase of oxygen

coverage and layer length enhances interfacial shear force. Further increase of oxygen coverage to

about 7% leads to a saturated interfacial shear force. A model was also established to demonstrate

that the mechanism of interfacial load transfer consists of two contributing parts, including the

formation of new surface and relative sliding along the interface. These results are believed to be

useful in development of new graphene-based nanocomposites with better interfacial properties.VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4870170]

I. INTRODUCTION

The reinforcement-matrix interface plays a critical role

in dictating the mechanical performance of composites as it

affects the effectiveness of interfacial load transfer while

loading.1–4 To explore the interfacial behaviour, direct pull-

out experiment has been applied to short-fiber and carbon

nanotube reinforced composites.5–8 For graphene-polymer

composites, however, the unique shape and dimensions of

graphene make the direct pull-out test a technical challenge.

Raman spectroscopy and atomistic simulation are considered

to be possible alternatives. Using stress-sensitive graphene

G’ band, load transfer along the graphene-polymer interface

was evaluated using Raman spectroscopy.9–12 In combina-

tion with shear-lag theory,13,14 Gong et al.9 reported a rela-

tively low level of interfacial shear stress (�5 MPa) between

graphene and polymer, which is an order of magnitude lower

than that between carbon nanotube (CNT) and polymer

(�40 MPa).15 In contrast, Srivastava et al.12 showed that gra-

phene may provide higher load-transfer effectiveness than

CNT. Up to now, the interfacial behaviour and the underly-

ing reinforcement mechanisms in graphene-polymer nano-

composites have not been well understood. On the other

hand, atomistic simulation of interfacial behaviour in

graphene-polymer composites is lacking although it has been

used in CNT-polymer nanocomposites.16–19 Experimentally,

it has been confirmed that a strong graphene-polymer inter-

face enables excellent mechanical properties of graphene-

polymer nanocomposites and can be obtained by introducing

covalent bonding between graphene and polymer.20 Rafiee

et al.21 and Zaman et al.22 reported enhanced fracture and fa-

tigue properties of nanocomposites by functionalized gra-

phene sheets. Ramanathan et al.23 found functionalized

graphene sheet has a strong interfacial interaction with the

polymer matrix, confirmed also by the observation of Yang

et al.24 However, the reinforcing mechanism of functional-

ized groups on load transfer along graphene-polymer inter-

face has not been investigated.

In this work, we conducted molecular dynamics (MD)

simulations to simulate the pull-out of graphene from poly-

mer and effects of surface functionalization on the interfacial

load transfer. Both influences of coverage degree of surface

functionalization and graphene layer length on interfacial

shear force and interfacial shear stress during pull-out were

investigated. A theoretical model was established to under-

stand the reinforcing mechanism of surface functionalization

(e.g., doping hydrogen and oxygen atoms to graphene) on

interfacial load transfer.

II. MATERIALS AND METHODS

A. Molecular dynamics models

The pull-out of graphene from polymer matrix was

simulated using MD method. Polyethylene (PE) was chosen

due to its structural simplicity, which can effectively reduce

the computational cost. To set up the atomistic structures,

three-dimensional (3D) periodic models of PE layer

were first established using Material Studio (Accelrys, Inc)

with the dimensions of L (length)�W (width)� T

a)Author to whom correspondence should be addressed. Electronic mail:

[email protected]

0021-8979/2014/115(12)/123520/6/$30.00 VC 2014 AIP Publishing LLC115, 123520-1

JOURNAL OF APPLIED PHYSICS 115, 123520 (2014)

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(thickness)¼ 5–30 nm� 5 nm� 3 nm. The PE layers consist

of 25–150 molecules, and each molecule (CH3-(CH2-CH2)59-

CH3) is composed of 60 monomers. As shown in Fig. 1(a),

the simulation cells were constructed by sandwiching mono-

layer graphene (Model 1), bi-layer graphene (Model 2),

hydrogen-functionalized monolayer graphene (Model 3), and

oxygen-functionalized graphene (Model 4) between two PE

layers. h represents the equilibrium distance between graphene

and PE matrix. In Model 3 and Model 4, 3% hydrogen and

1–10% oxygen were regularly patterned on both sides of

graphene monolayers, as shown in Figs. 1(b)–1(e). For the

possible dimension effect of PE layers, our simulations dem-

onstrated that there is no obvious difference of interfacial

shear force when varying width and thickness. Hence, only

one width (5 nm) and thickness (3 nm) were considered in this

work. As for the effect of PE chain length, previous study

demonstrated that there is also unobvious variation of PE dis-

tribution in the vicinity of polymer-PE interfaces with PE

chain length (n ranging from 40 to 250).25 Therefore, only PE

molecule of 60 monomers was chosen for simulation simplic-

ity here.

An ab initio polymer consistent force field (PCFF)26,27

was employed to calculate the atomistic interactions between

graphene and PE. Open-source code LAMMPS28 was used

for the MD simulations as it has been broadly adopted for

modelling graphene29–31 and carbon-based polymer

nanocomposites.32–38 In general, the total potential energy of

a simulation system can be expressed as

Etotal ¼ Ebond þ Eover þ Eval þ Etors þ EvdW þ ECoulomb; (1)

where Ebond, Eover, Eval, Etors, EvdW, and ECoulomb are the

energy components corresponding to bond, overcoordina-

tion, angle, torsion, Van der Waals (vdW), and Coulomb

interactions, respectively. The detailed expression for each

component can be found elsewhere.37 The cut-off distances

of both vdW and Coulomb interactions were chosen as 1 nm

in the simulations.37

To obtain an equilibrated structure, each unconstrained

model was placed into a constant-temperature, constant-pres-

sure (NPT) ensemble for 20 ps and then a constant-

temperature, constant-volume (NVT) ensemble for another

500 ps at the temperature T¼ 100 K, pressure P¼ 1 atm and

time step Dt¼ 1 fs after the initial energy minimization.

After 500 ps calculation at T¼ 100 K, the unit-cell models

are expected to be fully equilibrated. The equilibrium dis-

tance between the graphene and PE layer (h) can be esti-

mated numerically or theoretically. In the Model 1, the

equilibrium distance is numerically estimated as 2.81 A.

B. Pull-out simulation

For the simulation of pull-out process, non-periodic

boundary conditions (non-PBCs) were first introduced at

each end of the graphene layers along x axis by adding

hydrogen atoms to eliminate unsaturated boundary effect.

Then, the graphene layers in all four models were pulled out

from the PE matrix via displacement increment (Dx¼ 0.1 A)

along x axis while keeping PE layers relaxed. The pull-out

process of Model 1 is shown in Fig. 2, which is similar to

that of Model 2 (not shown in Fig. 2).

Assuming no cross-link between graphene and PE, vdW

interaction is expected to dominate the interfacial bonding.

To understand the load transfer along a graphene-polymer

interface, the interfacial shear force (FGP) and interfacial

shear stress (sGP) need to be evaluated. In the pull-out simu-

lations, FGP was estimated by the change of vdW interaction

along the interface, i.e., FGP ¼ �@Eint=@X, where Eint is

vdW interaction energy; X is pull-out displacement of gra-

phene. For a given FGP-X curve, the interfacial shear stress

can be calculated by using sGP ¼ 1=Wð Þ@FGP=@X, where Wis the width of graphene nanofiller along y axis.

Due to the discrete arrangement of atoms at graphene-

PE interfaces, relative sliding between graphene and PE may

influence the interfacial shear force during pull-out. To

investigate the relative sliding between graphene and PE

FIG. 1. (a) Equilibrated atomistic model of monolayer graphene-PE nanocomposite, (b) monolayer graphene (Model 1), (c) bi-layer graphene (Model 2),

(d) monolayer graphene functionalized by hydrogen atoms (Model 3), and (e) monolayer graphene functionalized by oxygen atoms (Model 4). (In PE matrix:

C-green; H-blue. In graphene: C-orange; H-blue; O-red).

123520-2 Wang et al. J. Appl. Phys. 115, 123520 (2014)

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matrix, periodic boundary conditions (PBCs) were intro-

duced to both ends of model cells along x axis (Fig. 1).

III. RESULTS AND DISCUSSION

A. Theoretical analysis of pull-out process

During pull-out, interfacial shear force is generated by

two physical mechanisms.39 One is the relative sliding

between the carbon atoms of graphene and the polymer

chains. The magnitude of interfacial shear force is largely

dependent on the local arrangement of the atoms along the

interface. For example, Chen et al.40 reported a non-zero

interfacial shear stress (�1.0 MPa) between the walls of

double-walled CNT during pull-out. The second mecha-

nism is due to the formation of new surface when graphene

layer is pulled out from the polymer.41 By investigating the

relative sliding along the interface, our MD simulation con-

firmed the presence of non-zero interfacial shear stress sGM,

as shown in Fig. 3. The amplitude of sGM fluctuates during

relative sliding. This is caused by the discrete arrangement

of molecular chains in PE. Based on Fig. 3, it is reasonable

to assume a sinusoidal distribution of sGM, and then we

have

sGM xð Þ ¼ s0GM sin Du xð Þ=2pl0

� �; (2)

where s0GM is the average amplitude of sGM; Du(x)¼ uG(x)

� uPE(x) is the relative sliding displacement between gra-

phene uG(x) and PE uPE(x); and l0� 4.3 A is the correspond-

ing periodic length between two sinusoidal peaks. As both

graphene and PE are assumed to be rigid during relative

sliding, the displacement of PE can be regarded as zero, and

Eq. (2) can be rewritten as

sGM xð Þ ¼ s0GM sin uG xð Þ=2pl0

� �¼ s0

GM sin X=2pl0ð Þ: (3)

If the PE matrix is subjected to a tension load, the axial

force is expected to be transferred to graphene via the

graphene-PE interfaces. As graphene is much stiffer than PE

matrix, the axial force will be mainly borne by graphene

layers. In equilibrium, the interfacial shear force per unit

width FGP can be expressed as

FGP ¼ Fc þ 2W

ðL

0

sGMdx; (4)

where Fc is the interfacial shear force caused by the forma-

tion of new surface; 2WÐ L

0sGMdx is the interfacial shear

force caused by the relative sliding between graphene and

PE. From Eqs. (3) and (4), FGP can be integrated and rewrit-

ten as

FGP ¼ Fc þ 2Ws0GM sin X=2pl0ð ÞL: (5)

According to Eq. (5), FGP varies as a function of both Xand L. Since the maximum value of jsinðX=2pl0Þj equals 1,

the maximum value of FGP can be estimated as

FmaxGP ¼ Fc þ 2Ws0

GML: (6)

B. Interfacial shear force and shear stress

We evaluated the total interfacial shear force and shear

stress during pull-out using MD simulation. For reasonable

comparison of interfacial shear stress between different

cases, interfacial shear force FGP is normalized by W in the

following discussions. Figs. 4(a)–4(d) shows the variation

of FGP/W in Models 1–4 at L¼ 10 nm. Notably, the value of

FGP/W varies periodically with the pull-out displacement X,

consistent with the Eq. (5). This feature can be also

observed in the (FGP/W)-X curves for the graphene layers

with different lengths (L¼ 15–30 nm). Taking the average

values of FGP/W in Figs. 4(a)–4(d), the (FGP/W)�X curves

for Models 1–4 are redrawn and shown in Fig. 4(e).

Obviously, there are three different stages in the

(FGP/W)�X curves for models 1 and 2 (monolayer and

bi-layer graphene). The length of both stages I and III is

FIG. 2. (a)–(d) Snap shots of pull out of monolayer graphene from PE ma-

trix. Red dash lines shown in (b)–(d) highlight the recovery of deformed

polymer layers after graphene being pulled out.

FIG. 3. Interfacial shear stress sGM induced by the relative sliding between

graphene and PE matrix.

123520-3 Wang et al. J. Appl. Phys. 115, 123520 (2014)

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approximately 1 nm, which is close to the cut-off distance

of vdW interaction selected in the simulations. At stage I,

FGP/W increases quickly with X, due to newly formed sur-

face of graphene after pull-out from the polymer matrix.

Then, FGP/W stays almost constant at stage II, due to the

fact that the length of newly formed surface interacts with

the polymer at a constant cut off distance, i.e.,1 nm from

the pull-out end. The deformed polymer layers behind gra-

phene are recovered when the graphene layer is pulled out,

as shown in Fig. 2.

For model 4, FGP/W rises at Stage I. Then, it is interest-

ing to note that FGP/W at Stage II reduces with the pull-out

displacement X. The possible reason is due to the change of

atomistic configurations subjected to interfacial shear force.

As shown in Fig. 5, some PE molecular chains are attached

to graphene layer after being pulled out from the PE matrix,

which may result in lower �@Eint=@X and lower FGP. Recent

experimental investigation has confirmed that functionalized

graphene can improve interfacial adhesion on polymer surfa-

ces.23 According to Fig. 4, it is more efficient to adopt

FIG. 4. (a)–(d) Normalized interfacial

shear force FGP/W as a function of

pull-out displacement (L¼ 10 nm), and

(e) averaged FGP/W as a function of

pull-out displacement X.

FIG. 5. Snap shots of complete pull out of monolayer graphene with oxygen

coverage of 3% (Model 4). Dotted lines highlight the PE chains attached on

the graphene layer.

123520-4 Wang et al. J. Appl. Phys. 115, 123520 (2014)

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oxygen functional groups rather than hydrogen to enhance

the interfacial strength.

The total interfacial shear stress, i.e., sGP ¼1=Wð Þ@FGP=@X only presents at the ends of the embedded

graphene, where (FGP/W)�X curves have non-zero slopes,

Fig. 4(e). Assuming a linear distribution of FGP at both

stages I and III, a constant value of sGP can be obtained. By

solving the integral equation FmaxGP ¼ 2W

Ð XI

0sGPdx, the value

of sGP can be obtained as

sGP ¼ FmaxGP =W

� �=2XI; (7)

where XI is the distance corresponding to the FmaxGP =W

� �at

the stage I. Fig. 6 shows the distributions of interfacial shear

stress sGP. Table I lists the estimated sGP using Eq. (7), cor-

responding to different graphene lengths. It is clear that the

shear stress increases with the length. The estimated sGP for

monolayer graphene with a length of 10 nm is 140 MPa,

larger than that between CNT and PE matrix around

100 MPa.17 This indicates that the interface strength between

the graphene layer and PE may be higher than that between

CNT and PE, implying higher reinforcement efficiency in

graphene-PE composites.

C. Effect of graphene length and surfacefunctionalization on interfacial shear force

As shown in Fig. 7(a), FmaxGP =W increases with graphene

length L. Therefore, increase of L is an effective way to

improve interfacial load transfer. According to Eq. (6), the

value of 2s0GM is the slope of Fmax

GP =W� �

� L curves. By

curve fitting in Fig. 7(a), s0GM in model 1–4 were estimated

to be 4.34 MPa (Model 1), 5.16 MPa (Model 2), 16.16 MPa

(Model 3), and 35.28 MPa (Model 4). These values of s0GM

are very close to those directly extracted from Fig. 3, e.g.,

3.77 MPa (Model 1) and 5.42 MPa (Model 2). It can be

observed that s0GM in Model 4 is much higher than those in

Model 1–3. For the normalized interfacial shear force Fc/Wdue to the formation of new surface, the value of Fi

c=W in

Model i (i¼ 1–4) is in the order of F4c=W > F2

c=W > F3c=

W � F1c=W. Both bi-layer and oxygen functionalization can

significantly increase Fc. Therefore, higher s0GM and Fc lead

to a stronger interfacial interaction between O atoms and

PE matrix during pull-out. Corresponding to graphene

length, L¼ 10 nm, FmaxGP =W in the bi-layer graphene and

monolayer graphene with H atoms and O atoms is increased

by 36.4%, 48.6%, and 183%, respectively. The highest

FmaxGP =W is associated with oxygen-functionalized graphene.

Chemical functionalization with O atoms (or maybe other

functional groups) suggests another efficient method of

reinforcing interfacial load transfer. It can be concluded

that the improved interfacial load transfer by chemical

functionalization lies in the stronger vdW interaction.

The effect of oxygen coverage on graphene layer on

FmaxGP =W is shown in Fig. 7(b). It can be seen that Fmax

GP =Wincreases approximately linearly with O coverage up to

7% and then becomes saturated, implying the ineffective-

ness of load transfer at higher oxygen loading. The possi-

ble reason is considered to be the excessive oxygen

causing the reduction of the period of relative sliding

between oxygen and PE atoms during pull-out, which

leads to reduced fluctuation of vdW energy and therefore

reduced shear force.

FIG. 6. (a) Schematics of pull-out of monolayer graphene from PE, (b) dis-

tribution of sGP in Models 1–3, (c) distribution of sGP in Model 4.

TABLE I. Interfacial shear stress, sGP (MPa).

LengthModel 1 Model 2 Model 3 Model 4

(nm) Stages I & III Stages I & III Stages I & III Stage I Stage III

10 140 191 208 396 190

15 152 209 250 451 210

20 166 215 278 521 220

25 173 229 320 605 240

30 194 235 375 760 260

FIG. 7. Normalized maximum value of

interfacial shear force FmaxGP =W as a

function of (a) graphene length L(Models 3 and 4 have hydrogen and

oxygen coverage of 3%) and (b) oxy-

gen coverage.

123520-5 Wang et al. J. Appl. Phys. 115, 123520 (2014)

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IV. CONCLUSION

To understand interfacial load transfer and reinforce-

ment mechanism of surface functionalization in graphene-

polymer nanocomposites, we systematically simulated the

pull-out of graphene from polymer. The effects of coverage

degree of surface functionalization and graphene layer length

on interfacial load transfer were investigated. Both theoreti-

cal and numerical analyses confirmed that the interfacial

shear force is caused by the formation of new surfaces and

the relative slides between graphene and polymer atoms

along the interfaces. The interfacial shear force and stress

get enhanced with the increase of coverage degree and length

of graphene layer, indicating that surface functionalization is

an effective way to increase the interfacial shear force during

pull-out. As compared to monolayer graphene, about 48%

and 183% increase of interfacial shear force were observed

in the graphene layer with hydrogen and oxygen fictionaliza-

tion of 3%. Further increase of oxygen coverage to about 7%

led to a saturated interfacial shear force.

ACKNOWLEDGMENTS

The authors would like to thank Dr. Yuli Chen from

Beihang University (China). M. C. Wang thanks the

QUTPRA scholarship from Queensland University of

Technology. This work is partly supported by the research

fund from National Natural Science Foundation of China

(No. 11372104) to N. Hu. We also acknowledge the HPC

center in Queensland University of Technology for access to

its computation resources.

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